In this note the complex conjugate spin connections (1) and (2) are given for plane waves and B(3) theory. These are maps of the aether or vacuum. They were computed by co author Horst Eckardt using the equations of conservation of antisymmetry for B(3) theory, nominated for a Nobel prize several times. For plane waves the Lindstrom constraint reduces to Eq. (14). The Lindstrom constraint is the trace antisymmetry law of physics. It is written self consistently with the vector antisymmetry laws of physics, Eqs. (11) to (13). The trace antisymmetry law and scalar antisymmetry law (15) must be solved simultaneously and self consistently. This is achieved by defining A*(total) as in Eqs. (20) to (23). This procedure means that the homogeneous field equations (16) and (17) are obeyed automatically on the ECE2 level in physics. For plane waves the electric field strength E is known so the scalar potential for plane waves can be found from Eq. (24), knowing the spin conenction vector. Then the scalar spin connection can be found from the Lindstrom constraint. This is another map of the vacuum for B(3) theory. Maps of the vacuum exist for any theory of physics on the ECE2 level. Finally the scalar antisymmetry law (26) must always be obeyed. This can always be achieved by using the gauge transformation (27), and by adjsuting the gauge function chi. Antisymmetry conservation is a major discovery in physics, as was B(3). So this note can be used in Section 3 of UFT388 The gauge procedure is new to this note, and can also be used in gravitation on the ECE2 level. This is far in advance of the standard model.

This is very good progress, the vector antisymmetry equations have been solved to give the vector spin connection:

omega = (kappa / root2) (i bold – i j bold) exp i phi – i kappa k

I agree that this is the correct spin connection. I will rework the note with this spin connection and send the new calculations over to Horst. The final calculations can be used in Section 3 of UFT388, because UFT389 is on gravitation.

When using the computer, there seem to be some problems with antisymmetry eqs. (32-34). The derivative

partial A_y* / partial z

is not zero. Therefore omega_z cannot be zero in (38). The eq. (42) with

i kappa = kappa

means that kappa=0, not omega_z=0.

By computer, using A* = A(2) = ,

it follows that the equation set (32-34) is of rank 2. The solution is
with an unspecified constant r2. This looks a bit strange. Some tests led to the result that

omega =

solves the antisymm. eqs. (32-34). However with omega_z=0 it does definitely not.
The subsequent calculation gives for E and B (total fields):

There are some differences in signs with eq. (53). The B_Z component (which should be equal to B(3)) is imaginary.
Maxwell’s equations give div E=0 and div B=0 but non-vanishing current densities.
The Lindstrom constraint for phi = 0 gives
(should be zero). For phi* given by (62) the equation

follows.
It seems that some adjustments have still to be done for this note, or I misunderstood some parts.

Horst

Am 24.09.2017 um 14:07 schrieb EMyrone:

This theorem defines the B(3) field as in Eq. (24) through the conjugate product of spin connection plane wave vectors. Symmetry shows that omega(3) = A(3) = 0. The vector antisymmetry equations (32) to (34) are obeyed, and the other two antisymmetry equations (46) and (47) are obeyed by using the procedure on pp. 8 and ff. of the Note. This is the best procedure to adapt in every application because it makes sure that the two antisymmetry equations (46) and (47) are obeyed simultaneously and self consistently. So B(3) theory rigorously conserves antisymmetry, as must all theories of physics. There is also a gravitational and fluid dynamical B(3) field. The ECE School of Thought has become independent of the standard model and is forging ahead with rapid advances.

Many thanks as ever for checking this note. These spin connections, Eqs. (13) to (16), are maps of the aether for a precessing planar orbit and it would be very interesting to graph the scalar and vector parts of the spin connection four vector for forward and retrograde precession. Then Q can be found and graphed from Eqs. (3) to (5), and omega sub 0 from the Lindstrom constraint (6), using the Newtonian gravitational scalar potential phi cap. Finally we use Eqs. (7) and (8). A lot of very interesting results will emerge.

There is a factor missing in the denominators of eqs.(13,14). The right solution (13) is:

And correspondingly for (14).

Horst

Am 22.09.2017 um 13:19 schrieb EMyrone:

This not gives the spin connections for a forward and retrograde precession using the gravitational potential (3). The results are equations (13) to (16) and can be graphed. They are maps of spacetime, the vacuum or gravitational aether. In order to compute the vector potential Q it is necessary to compute Eqs. (17) to 919), the antisymmetry equations. Having found the vector potential, the scalar spin connection is found from the Lindstrom constraint,and finally the total vector potential found as in the previous note. If it is assumed that the spin connection is two dimensional for a planar orbit, the omega sub Z = 0. Computer algebra can be used to solve Eqs. (17) to (19), which are three simultaneous differential equations. I will look for a simple solution by hand. The differential equations are of the type dy / dx = f(x, y)y and so on. I am sure that there are code packages that can integrate such equations (e.g. Maxima, Mathematical,Maple, NAG, IBM ESSL, and so on) . A great deal of new information about precessing planar orbits will emerge from this complete theory, which in general is a new type of cosmology.

It is well known that there has been a severe decline in the quality of Vice Chancellors since Sir Thomas Parry and Sir Goronwy Daniel. The latest one, April McMahon, received a great deal of money from the tax payer, but several petitions were signed for her resignation. This is no good at all for Wales, every Vice Chancellor should be of the quality of the great scholar Sir Thomas Parry, (“Gwaith Dafydd ap Gwilym”). Every one must be a native of Wales and fluent in Welsh and be completely and deeply committed to Wales, and not to their bank account. I tried to find out how she was appointed, but the College refused to give any information to the freedom of information Commissioner. Gareth Evans and I would make far better Vice Chancellors, even if we sat on our butts on the pier, grinning and doing nothing, because we do all our work free. McMahon’s h index is 22, just enough for a full professor. Mine is 42 plus a vast and famous impact via scientometrics. AIAS / UPITEC has an impact of 53,132 page views per month per author compared with 233 for Aberystwyth. It is obvious that the system locks out the best scholars from Wales, and does not even attempt to find them. It is in need of sweeping and complete reform. It has no correlation at all between native Welsh speaking merit and reward. McMahon received a pay rise of £13,000 in her first year, and a pay off of £102,489 amid many calls and petitions for resignation. Staff morale is at rock bottom, having fallen off the pier. Universities in Wales should be much smaller, rigorously and completely bilingual, and put the language before everything. There are huge student fees imposed on the working classes of Wales to pay the huge salaries of mediocrities who never learn a word of Welsh. The h index of my Ph .D. supervisor, the late Prof. Emeritus Mansel Davies, is currently 31. He began publishing in 1938. My Civil List Pension is £2,400 a year and I am a triple world record holder. A Vice Chancellor’s salary is £200,000 a year and achievements on behalf of Wales are sometimes difficult to find with an electron microscope. The Anglo Norman colonizers of Wales are like an old sow who eats her offspring. Jonathan Swift would have satired this scene to atoms.

Information for “Marquis Who’s Who”. I have updated my CV (attached) to include three Wolf Prize nominations this year for the 2018 Wolf Prizes in chemistry, physics and mathematics, nominations for honorary Fellowships and Doctorates, and a mention of about nineteen directorships and one group chairmanship held in the past. I would like to check whether I am included in Marquis Who’s Who in the World, 2018. “Principles of ECE, Volume Two” has been published (August 2017).

I plan to go through the experimental evidence for non Newtonian effects and map the vacuum for each effect with the application of the new antisymmetry techniques. The first was orbital precession, (Note 389(4)) the next is planned to be velocity curve of a whirlpool galaxy. This is the clearest and most well defined evidence for the fact that the Einstein theory fails completely. Several UFT papers have shown how ECE2 describes the velocity curve, and also chapter eight of “Principles of ECE” volume one, Eqs. (8.112) and (8.113) (UFT366). Purchase of “Principles of ECE” volumes one and two is strongly recommended. They are both excellently collated and produced, with colour illustrations.

In August 2017 the readings set a new record high, shattering the previous record set in July 2017. This month the total is headed for the second place in record highs, and in July 2017 the third place in record highs was recorded. This measn that the ECE School of Thought has become independent of the Standard Model of Physics.

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